The interaction between the Coriolis force and a wind farm wake is
investigated by Reynolds-averaged Navier–Stokes simulations, using two
different wind farm representations: a high roughness and 5
In recent years, wind farms have grown in size and are more frequently placed
in wind farm clusters. This means that large-scale effects are becoming more
important for wind turbine wake interaction in wind farms, and especially for
the interaction between wind farms. One large-scale effect that is often
neglected by wind farm modelers is the effect of the Coriolis force on wind
turbine or farm wakes. In previous work
The literature does not agree on the turning direction of wind farm wakes
caused by the Coriolis force.
The Coriolis forces change in the wake region and induce a clockwise
The present wind veer deflects the wind farm wake clockwise
Our goal is to clarify why the Coriolis force turns a wind farm wake
clockwise in the Northern Hemisphere. First, we test the hypothesis of
Note that this work is an extension of
In order to understand the interaction between the Coriolis force and a wind
farm wake, two RANS simulations of a simple rectangular wind farm of
5 25 wind turbines represented by ADs a high roughness of 1
The NREL 5 MW wind turbine has a hub height (
In the simulation where the wind farm is represented by a high roughness, a
roughness length of 1 m is chosen.
Rotated inlet profiles calculated by the precursor. Bottom plots are a zoomed view of the top plots. Rotor area is shown as black dashed lines.
The numerical setup of the RANS simulations with ADs including the Coriolis
force is fully described in previous work
Grid and boundary conditions of wind farm simulations. Every 16th
grid line is plotted.
Grid and boundary conditions of the single-AD simulation. Every fourth
grid line is plotted.
The same numerical grid is used in both wind farm simulations. The domain
definition including wind farm layout and boundary conditions (BCs) is shown
in Fig.
Stream-wise velocity at hub height, normalized by the free stream.
The numerical grid and boundary conditions of the single AD are shown
Fig.
Figure
In Fig.
Turbulence intensity at hub height.
The wind farm wake deflection is also visible in
Fig.
Stream-wise velocity subtracted and normalized by the free stream
In this section, the observed wind farm wake deflection from
Figs.
The momentum equation can be written as
The integrals are taken over square horizontal slices with an area of
The top and bottom figures show results from the simulation where the wind
farm is represented by 25 ADs and a high roughness, respectively. In
addition, the results from the left figures are taken from inside the wind farm,
while the right figures are made on the basis of the near wind farm wake. The results from
the wind farm simulation (solid lines) are compared with the results taken
from an empty domain (colored dashed lines). When the wind farm is not
present (colored dashed lines from Fig.
When the wind farm is represented by a high roughness
(Fig.
When the wind farm is represented by 25 ADs (Fig.
Figure
Stream-wise velocity at hub height, normalized by the free stream. Wind farm represented by 25 ADs. Contour line represents 95 % recovered velocity.
Stream-wise velocity at hub height, normalized by the free stream. Wind farm represented by a high roughness. Contour line represents 95 % recovered velocity.
Stream-wise velocity subtracted and normalized by the free stream
Stream-wise velocity at hub height, normalized by the free stream, for a single wake in a shallow ABL.
One could set the Coriolis force source terms to be constant in the
horizontal directions (also at the wind farm) to isolate the effect of the
wind veer on the wind farm wake deflection:
Contours of stream-wise velocity, subtracted and normalized by the
free stream, of a single AD operating in a shallow ABL are shown in
Fig.
Two RANS simulations of a wind farm including the effect of the Coriolis force are carried out that differ in wind farm representation. When the wind farm is modeled as a roughness change, the wind farm wake turns anticlockwise due to an imbalance in the Coriolis force. When the wind farm is represented by 25 actuator disks, the wind farm wake is deflected clockwise. An investigation of the momentum balance in the cross flow direction suggests that in the simulation with 25 actuator disks, the turbulence mixes momentum from above that has a relative wind direction towards the right, down into the wake region. When the Coriolis force is set as constant in the horizontal dimensions to isolate the effect of wind veer, the wind farm wake deflection of the 25 actuator disks is unaffected. This proves that the Coriolis force indirectly causes the wind farm wake to deflect clockwise because of the present wind veer and not because of the local changes in the Coriolis force; this is also confirmed by the simulation of a single actuator disk operating in a shallow atmospheric boundary layer. Hence, the interaction between the Coriolis force and a wind farm wake is a complex process that cannot be simplified to the interaction between the Coriolis force and a roughness change when the deflection of the wind farm wake is investigated.
The data presented can be made available by contacting the corresponding author.
The authors declare that they have no conflict of interest.
This work is supported by the Center for Computational Wind Turbine Aerodynamics and Atmospheric Turbulence funded by the Danish Council for Strategic Research, grant number 09-067216. Computational resources were provided by DCSC and the DTU central computing facility. Edited by: C. L. Bottasso Reviewed by: two anonymous referees